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Preprint (Author's original)arXiv.org - Non-exclusive license to distribute, Open
Preprint
Distribution of the Number of Corners in Tree--like Tableaux
08 Apr 2018
Abstract
In this paper, we study tree--like tableaux and some of their probabilistic
properties. Tree--like tableaux are in bijection with other combinatorial
structures, including permutation tableaux, and have a connection to the
partially asymmetric simple exclusion process (PASEP), an important model of an
interacting particles system. In particular, in the context of tree-like
tableaux, a corner corresponds to a node occupied by a particle that could jump
to the right while inner corners indicate a particle with an empty node to its
left. Thus, the total number of corners represents the number of nodes at which
PASEP can move, i. e. the total current activity of the system. As the number
of inner corners and regular corners is connected, we limit our discussion to
just regular corners and show that asymptotically, the number of corners in a
tableau of length $n$ is normally distributed.
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Details
- Title
- Distribution of the Number of Corners in Tree--like Tableaux
- Creators
- Pawel HitczenkoAleksandr Yaroslavskiy
- Resource Type
- Preprint
- Language
- English
- Academic Unit
- Mathematics
- Other Identifier
- 991020531956304721